Reduction formula for point group Td



Characters of input representation
E 8C3 3C2 6S4 6d
9 0 1 -1 3



Decomposition into Irreducible representations
A1 A2 E T1 T2 Total
1 0 1 0 2 4





Force field analysis


Allowed / forbidden vibronational transitions
Operator A1 A2 E T1 T2 Total
Linear (IR) 1 0 1 0 2 2 / 2
Quadratic (Raman) 1 0 1 0 2 4 / 0
IR + Raman - 0 - 0 2 2 / 0



Characters of symmetric powers for vibration representation
Force field Tensor
Order
E 8C3 3C2 6S4 6d
linear 1 9 0 1 -1 3
quadratic 2 45 0 5 1 9
cubic 3 165 3 5 -1 19
quartic 4 495 0 15 3 39
quintic 5 1.287 0 15 -3 69
sextic 6 3.003 6 35 3 119


Decomposition into Irreducible representations
Number of nonvanshing force constants
Force field Tensor
Order
A1 A2 E T1 T2
linear 1 1 0 1 0 2
quadratic 2 5 0 5 3 7
cubic 3 13 4 14 15 25
quartic 4 33 12 45 51 69
quintic 5 72 39 111 141 177
sextic 6 162 101 257 342 400


Literature




Character tables for chemically important point groups Character table for point group Td Jacobs University Bremen

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement